1. Field of the Invention
The invention relates to a method for modelling the spatial distribution of geometric objects in a discontinuous environment, such as, for example, fault networks in a geologic formation.
The method according to the invention, when applied to the study of the subsoil for example, can notably serve to optimize the production from oil reservoirs at different stages of their development.
2. Description of the Prior Art
Engineering techniques for naturally fractured subsurface reservoirs are simply based on the geometric characterization of their fracture networks. There is a lack of tools specially designed for this purpose and suited to the petroleum geologic context. Through lack of such tools, the results of geologic expert evaluations cannot be quantified in terms that are workable by reservoir engineers.
Knowledge of the distribution of the fractures in a geologic formation is of great importance first for optimizing the location and the spacing between the wells that are to be drilled through an oil formation.
Furthermore, the geometry of the fracture network conditions influences the displacement of fluids on the reservoir scale as well as on the local scale, where it determines the elementary matrix blocks in which the oil is trapped. Knowledge of the distribution of the fractures is thus also very useful at a later stage for the reservoir engineer who wants to extrapolate the production curves and to calibrate the models simulating reservoirs.
The development of naturally fractured reservoirs thus requires better knowledge of the geometry of the fracture networks and of their contribution to the orientation of the flows.
It is known that two aspects have to be taken into account when it is desired to model a naturally fractured reservoir from a geometric as well as from a geologic point of view: the scale effect and the genesis of the fractures.
Multiscale analysis techniques such as the fractal analysis are increasingly used currently, which shows that the scale effect is one of the major difficulties encountered when dealing with fractured environments.
It is known that, whatever the observation scale may be, an area appears discontinuous because of the relatively large fractures in relation to the dimensions of this area. A nearly unlimited range of different fracture sizes can be found in a reservoir.
When the flows are modelled on the scale of a reservoir, the major faults, drain holes or barriers, are explicitly considered. Fractures of a smaller size can be taken into account by bringing in an equivalent continuous environment exhibiting so-called double porosity characteristics. In order to determine the characteristics of this equivalent virtual environment, it is however necessary to consider explicitly the geometry of the system of fractures, whereas the network of pores and of microcracks is defined by means of the equivalent continuous environment referred to as a "rock matrix". Whatever their size category, fractures play a part in a given fluid flow process.
Besides this scale effect, it is also known that there is a relationship between small-size and large-size discontinuities. Major faults for example can be the result of the coalescence of minor faults. It is also known that a certain type of fracturing related to folds is associated with the structure of the field as well as with major faults in the case of a roll-over. The analysis of a configuration of fractures on a given scale must integrate geologic characteristics on different scales because the fractures observable on all scales are connected with one another.
It appears that most of the fault networks observed, particularly in petroleum geology, are incomplete because the measuring tools used only detect the largest faults. The minor faults of lower extension, which can nevertheless play an important part in the circulation of fluids, remain inaccessible for observation.
It has been shown in the last few years that certain natural fault networks exhibit fractal properties because of the chaotic geometry, as shown notably in the different documents listed hereafter:
Walsh J. J. and J. Watterson, Population of Faults and Fault displacements and their Effects on Estimates of Fault-Related Regional Extension, in J. Struct. Geol.; 14, 701-712, 1992;
Davy P. and al, Some Consequences of a Proposed Fractal Nature of Continental Faulting, Nature, 348, 56-58, 1990.
New techniques for predicting the geometry of so-called subseismic minor faults have been presented, notably by:
Gauthier B. D. M. et al, Probabilitic Modelling of Faults Below the Limit of Seismic Resolution in Pelican field, North Sea, offshore United Kingdom, The AAPG Bulletin, Vol.77, No.5, pp. 761-777, 1993.
They mainly generate fault geometries randomly through an extrapolation of the known distribution of the fault lengths, calibrated on a so-called "fractal" distribution of lengths.
It should however be noted that the modelling of minor faults in a known geometry of major faults, allowed by applying well-known techniques, does not lead to entirely satisfactory and representative results because the fault network obtained does not have a sufficiently strict fractal nature.